Answer:
y - 5 = [tex]\frac{3}{2}[/tex](x - 1)
Step-by-step explanation:
Note that [tex]\frac{dy}{dx}[/tex] = [tex]m_{tangent}[/tex]
Differentiate using the power rule
[tex]\frac{d}{dx}[/tex](a[tex]x^{n}[/tex]) = na[tex]x^{n-1}[/tex]
Given
y = x[tex]\sqrt{x}[/tex] = x. [tex]x^{\frac{1}{2} }[/tex] = [tex]x^{\frac{3}{2} }[/tex], then
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{3}{2}[/tex][tex]x^{\frac{1}{2} }[/tex]
When x = 1
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{3}{2}[/tex] . 1 = [tex]\frac{3}{2}[/tex]
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = [tex]\frac{3}{2}[/tex] and (a, b) = (1, 5), thus
y - 5 = [tex]\frac{3}{2}[/tex](x - 1) ← equation of tangent
